Geometric analysis of historical violin outlines: A study of approximation by circular arcs

Details

Supervisors

Glineur, François ; Ceulemans, Anne-Emmanuelle

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil en mathématiques appliquées, à finalité spécialisée

Abstract

enViolins that are constructed nowadays are copies of existing models. It is believed that luthiers from the 17th and 18th centuries designed the outline of violins using circles. We will here attempt to approximate the outline of historical violins using a set of circles. We are using a corpus of 14 violins from the Low Countries, as well as a synthetic violin made of circles, as reference. We first analyze the performance of a greedy algorithm that builds circles sequentially around the contour, bounded by a user-defined tolerance. Second, we develop a global optimization method, where a predefined number of circles is optimally selected out of a set of candidate circles, built by least-squares approximation of local neighbourhoods of points of the contour. Three different variations of this second method are explored. We evaluate those methods with error-based metrics, as well as a symmetry score. The greedy algorithm produced poor results, as it is heavily conditioned on the starting point. The global optimization methods resulted in recurring patterns across the violin corpus. While these results do not constitute proof of historical evidence, they can form a basis for future organological research.